We show that the only topological and algebraic copies of
N* to
be found in N* are the trivial ones, namely
k⋅N* for k∈ N. A similar
statement holds for copies of Z*
in Z*. As a
consequence, we obtain the
corollary that N*
contains no copies of Z* whatever.

Acknowledgements

The first author gratefully acknowledges support received from the
National Science Foundation via grants DMS 9025025 and DMS 9424421.

Both authors gratefully acknowledge support received from EPSRC for the
visit during which this research was conducted.